The optics will display the dot so that it represents an axis that is parallel to your chosen line of sight (chosen when you zeroed it). There is no parallax in a good reflex sight (who knows about the cheap ones? I stay away from them). What you are seeing is that line-of-sight axis shifting as your eye shifts, but it keeps the exact angle with respect to the barrel bore (always parallel to your chosen line-of-sight). Therefore there is in fact an aiming error introduced when you have the sight zeroed by looking through the center of the sight, and then move your aiming eye off from center. However, this error is a maximum of half the width of the sight's viewing area (15 mm maximum error in a 30 mm circle, for example) no matter the distance.
This is not parallax, but something similar and less serious.
In use, you will not ever notice this small potential error unless you're trying to punch holes in dimes. The whole idea of the thing is that you can completely forget about your sight and spend all your attention on the target and the magic, floating dot! Target and dot appear on the same focal plane, which is another major advantage. I would consider a reflex sight as good as iron sights for accuracy, and at the same distances, for slow fire, but much faster and easier to use for rapid shooting at targets of opportunity, and useable in a much wider range of lighting conditions.
Just use it and you will see.
If you want an exhaustive explanation, take a look at my article on the subject. Grab a cup of coffee and take your time:
http://www.ultimak.com/UnderstandingE-sights.htm
But I would recommend going to the range first and trying the thing, so you have that experience under your belt, or you may just end up more confused.
Holographic sights are a little different, technically, but in use you will notice no differences except for that wonderful 1 MOA dot and 65 MOA circle reticle.
Both technologies are becoming commonplace in military units. All the major manufacturers have had to scramble to keep up with the military demand in recent years.